Problem: Keenan wants to make a paperweight at pottery class. He designs a pyramid-like model with a base area of $80$ square centimeters and a height of $7.5$ centimeters. The density of the clay he is using is $1.7$ grams per cubic centimeter. What is the weight of Keenan's paperweight?
Explanation: This is a density word problem. To solve it, we can use the following equation, which is the volume definition of density: ${\text{Density}}=\dfrac{{\text{Total quantity}}}{{\text{Volume}}}$ What do we know? The ${\text{density}}$ of the clay is ${1.7}$ grams per cubic centimeter. The base area of the pyramid-like paperweight is $80$ square centimeters and its height is $7.5$ centimeters (we can use this to find the ${\text{volume}}$ ). What do we need to find? The paperweight's weight, which is the ${\text{total quantity}}$. The ${\text{volume}}$ of the pyramid-like paperweight is $\dfrac{1}{3}\cdot 80\cdot 7.5={200}$ cubic centimeters. Let's denote the weight as $ w$. Now we can plug ${\text{density}=1.7}$, ${\text{total quantity}=w}$, and ${\text{volume}=200}$ in the equation. $\begin{aligned} {\text{Density}}&=\dfrac{{\text{Total quantity}}}{{\text{Volume}}} \\\\ {1.7}&=\dfrac{{w}}{{200}} \\\\ {200}\cdot{1.7}&=\dfrac{{w}}{\cancel{{200}}}\cdot\cancel{{200}} \\\\ 340&= w \end{aligned}$ The weight of Keenan's paperweight is $340$ grams.